Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
1252 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C41 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C41 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#3549 | C2 | semidirect |
| 2. C41×#3151 | C2 | semidirect |
| 3. C41×#1655 | C2 | semidirect |
| 4. C41×#1525 | C2 | semidirect |
| 6. C41×H(3,𝔽4) | C22 | semidirect |
| 11. C2×#127×C41 | C22 | semidirect |
| 12. C41×#496 | C22 | semidirect |
| 15. C4×M16×C41 | C22 | semidirect |
| 16. C41×#329 | C22 | semidirect |
| 82. #19073 | C41 | direct (N × H) |
| 93. #3549 | C2×C41 | semidirect |
| 94. #3151 | C2×C41 | semidirect |
| 95. #1655 | C2×C41 | semidirect |
| 96. #1525 | C2×C41 | semidirect |
| 102. H(3,𝔽4) | C22×C41 | semidirect |
| 107. C2×#127 | C22×C41 | semidirect |
| 108. #496 | C22×C41 | semidirect |
| 111. C4×M16 | C22×C41 | semidirect |
| 112. #329 | C22×C41 | semidirect |
| 113. C41 | #19073 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3549 | 2 |
| C41×#3151 | 2 |
| C41×#1655 | 2 |
| C41×#1525 | 2 |
| #19073 | 41 |